Properties

Label 980.1.f
Level $980$
Weight $1$
Character orbit 980.f
Rep. character $\chi_{980}(99,\cdot)$
Character field $\Q$
Dimension $8$
Newform subspaces $5$
Sturm bound $168$
Trace bound $3$

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Defining parameters

Level: \( N \) \(=\) \( 980 = 2^{2} \cdot 5 \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 980.f (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 20 \)
Character field: \(\Q\)
Newform subspaces: \( 5 \)
Sturm bound: \(168\)
Trace bound: \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(980, [\chi])\).

Total New Old
Modular forms 24 18 6
Cusp forms 8 8 0
Eisenstein series 16 10 6

The following table gives the dimensions of subspaces with specified projective image type.

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 8 0 0 0

Trace form

\( 8 q - 4 q^{9} + O(q^{10}) \) \( 8 q - 4 q^{9} + 8 q^{16} + 4 q^{25} - 4 q^{29} - 4 q^{30} + 4 q^{36} - 4 q^{46} - 4 q^{50} - 4 q^{65} + 8 q^{74} - 4 q^{85} - 4 q^{86} + O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(980, [\chi])\) into newform subspaces

Label Dim. \(A\) Field Image CM RM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
980.1.f.a \(1\) \(0.489\) \(\Q\) \(D_{3}\) \(\Q(\sqrt{-5}) \) None \(-1\) \(-1\) \(-1\) \(0\) \(q-q^{2}-q^{3}+q^{4}-q^{5}+q^{6}-q^{8}+\cdots\)
980.1.f.b \(1\) \(0.489\) \(\Q\) \(D_{3}\) \(\Q(\sqrt{-5}) \) None \(-1\) \(1\) \(1\) \(0\) \(q-q^{2}+q^{3}+q^{4}+q^{5}-q^{6}-q^{8}+\cdots\)
980.1.f.c \(1\) \(0.489\) \(\Q\) \(D_{3}\) \(\Q(\sqrt{-5}) \) None \(1\) \(-1\) \(1\) \(0\) \(q+q^{2}-q^{3}+q^{4}+q^{5}-q^{6}+q^{8}+\cdots\)
980.1.f.d \(1\) \(0.489\) \(\Q\) \(D_{3}\) \(\Q(\sqrt{-5}) \) None \(1\) \(1\) \(-1\) \(0\) \(q+q^{2}+q^{3}+q^{4}-q^{5}+q^{6}+q^{8}+\cdots\)
980.1.f.e \(4\) \(0.489\) \(\Q(\zeta_{8})\) \(D_{4}\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{8}^{2}q^{2}-q^{4}-\zeta_{8}q^{5}-\zeta_{8}^{2}q^{8}+\cdots\)